7 papers · 1 filter
The basis number of 1-planar graphs
Saman Bazargani, Therese Biedl, Prosenjit Bose +2
Let be a set of Eulerian subgraphs of a graph . We say forms a -basis if it is a minimum set that generates the cycle space of , and any edge of lies in at mos…
On the -independence number in 1-planar graphs
Therese Biedl, Prosenjit Bose, Babak Miraftab
The -independence number of a graph is the largest possible size of an independent set in where each vertex of has degree at least in . Upper bounds for t…
Noncrossing Longest Paths and Cycles
Greg Aloupis, Ahmad Biniaz, Prosenjit Bose +7
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout. Short…
On 1-Planar Graphs with Bounded Cop-Number
Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari +1
Cops and Robbers is a type of pursuit-evasion game played on a graph where a set of cops try to capture a single robber. The cops first choose their initial vertex positions, and l…
Computing shortest paths amid non-overlapping weighted disks
Prosenjit Bose, Jean-Lou De Carufel, Guillermo Esteban +1
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of non-overlapping weighted disks in the plane. For a given parame…
Computing Vertex and Edge Connectivity of Graphs Embedded with Crossings
Therese Biedl, Prosenjit Bose, Karthik Murali
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of thi…
Approximating shortest paths in weighted square and hexagonal meshes
Prosenjit Bose, Guillermo Esteban, David Orden +1
Continuous 2-dimensional space is often discretized by considering a mesh of weighted cells. In this work we study how well a weighted mesh approximates the space, with respect to…